Not hostile in the least. I too think it is the basic distinction in philosophy, but I am trying to articulate it in a way that is, as you say, detached from a religious lexicon. (I know a little about how Heidegger might have thought about it, but I have hesitated about starting to read him because it is quite an undertaking.)
What prompts me, though, is that it is a distinction that seems completely lost on most people, and it seems to me to be one of the very first things that a philosophy should talk about. It seems to me to be first victim of nominalism, and nominalism came out the winner in the battle with realism. So there is the historical context. I think realism, in the medieval rather than the modern sense, is still nearer to the truth than nominalism. But the problem has always been, what does it mean to say that a universal 'exists'. People wonder 'where' they are or 'what' they are. But forms and universals don't 'exist somewhere': they simply show up in the way things happen.
Well, to a certain degree, I think that nominalism came out on top because its position contained more consistently demonstratable arguments, and in a period that placed a priority on the practice of ritual, this was decisive. Likewise, a later period that places a higher premium on practice (such as scientific practice) is more likely to opt for a form of nominalism.
I am hesitant about most ontological distinctions because it is often framed in an "us/them" dynamic. If the field of "existing things" vs. "beings" is limited to inanimate objects, this seems relatively harmless, unless it is used in an argument of ecological import. Then the distinction does not simply seem relevant, but is vital relevance. After all, if we are more ontologically significant than mere, let's say, trees, then the "well-being" of the surrounding foliage seems of lesser import than that of ourselves. The inviolable difference between us makes the common "interest" between ourselves and plant-life seem unconnected. I know that is not your intent, but it is an argument that often presents itself in similar situations.
In this case and in other, where is the line to be drawn between beings and existing things? As regards universals - mathematics, for example, which I know are of particular interest to you in regards this question: What distinguishes Mathematics (capital "m") from individual exercises of mathematical (lower-case "m") formulae. Mathematics may represent a certain form, or even language, of thought, that seem to require to operate in the same way regardless of circumstance to be meaningful. But there is evidence that these formulae do not "work" in the "same" way (like in certain problems in modern physics) where circumstances require a different interpretation of mathematical principles. (I'm not a physicist, so my POV is only a layman's.)
My point is that "being" is a notion of variable value. That was Aristotle's, the nominalists's, own conclusion. And perhaps it would be pragmatic, at the very least, to consider "being" as a value that might be reached by more than one means, at the very least, if not a variable value. I hope that this doesn't come off as harping, it's not. And I agree with you that it is a question of vital philosophic import. However, I think that it is a question who's answer will vary according to circumstance, as, perhaps, it should. I am sure that this seems like an ontologically inadequate, nominalist response; but I am afraid that any other response seems to me like to partake of the speculative or the mystical, and compresses several distinct concepts by which we shape the average experience. I know that experience is not limited to the "average experience". But if the ultimate experience is not accessible to the various perspectives that result in the average experience, by multiple routes, then I am not sure what warrant will ensure it's validity. In other words, I'm not sure that nominalism contradicts realism, but rather that it qualifies it.
Incidentally, if you are interested in reading some Heidegger, I recommend Basic Writings
, edited by David Farrell Krell. Heidegger was more of a hedgehog than a fox, so there are many points at which the remainder of his oeuvre is accessible, but that collection contains a number of reliably-translated, representative essays. I'm obviously a little down on Heidegger, but not because I'm not familiar with him, nor do I think he is unimportant. On the contrary, I think that a grasp of the philosophy, and the man, is important to a complete picture of 20th century philosophy.